So, I have a theory on why Sebastian 'hates' dogs.

Remember this scene? Where the dog died in Finny's arms?

After the dog died, Sebastian said "this is why I don't like dogs..."

I think he was hinting at the fact that at one point in time, he might have had a dog of his own, maybe before he was a demon, and when it died, his heart shattered. He was too heartbroken to ever get another dog again.